Explicit control of subgeometric ergodicity

This paper discusses explicit quantitative bounds on the convergence rates of Markov chains on general state spaces, under so-called drift and minorization conditions. The focus of this paper is on practical conditions that lead to subgeometric rates. Such explicit bounds are particularly relevant in applications where a family of Markov transition probabilities {Pθ : θ ∈ Θ} is considered and for which it is required to establish uniform-in-θ ergodicity. Examples of applications include stochastic versions of the popular EM algorithm (Expectation-Maximization) or adaptive Markov chain Monte Carlo (MCMC) algorithms (see [1] (resp. [14]) where quantitative bounds for geometric ergodicity (resp. geometric and subgeometric ergodicity) are used to establish the validity of the algorithms).

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